Appendix II 887 heat-weight^ Rankine the thermodynamic function, and Clausius the entropy ; the last term being now universally applied. We may now draw a diagram of heat changes by plotting r to a base of 0 as in Fig. 844, from which we may deduce Heat supplied or rejected = $ x mean r. Just as the fv curve shews work done, and is a cycle of mechanical operations, so the T<J> curve shews heat change, and is a cycle of thermal operations. It was first practically developed by Mr. J. McFarlane Gray, and its great value is apparent when one remembers how much heat is unrepresented on the j>v diagram; though both diagrams have their uses. Isothermals, having constant temperature, are horizontal straight lines on the ry diagram ; and adiabatics are vertical straight lines, for no heat is being supplied and yet T changes, <j> (r1-r2) = o and 0 = o, or entropy is unaltered (see Fig. 844). Applying to the Carnot cycle, Fig. 844, heat supplied is the area H1? and that rejected the area H2, for A B, c D are isothermals, and B c, D A adiabatics. Also the work done is Ht - H2 -T, «. . work done H, - BL r, - r<> .-. Efficiency = , — — — — - = .* - • 2 = l 2 heat expended Hx Ti To draw the r 0 diagram for water and steam, shewing heat supplied per Ib. weight, we commence with an arbitrary zero of entropy at 32° Fahr. =492° absolute. Then ! Entropy of water at 492° = o and at any otheil temperature r #w = loger~ from which Table I. (n,ext page) is calculated, and the results plotted as curve AB, Fig. 845, the area under which shews heat supplied up to any temperature. * Hyperbolic log. = comm on log. x 2 3026.